{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "kBQzOeY8Iaq3"
      },
      "source": [
        "# Bayesian Switchpoint Analysis\n",
        "\n",
        "\u003ctable class=\"tfo-notebook-buttons\" align=\"left\"\u003e\n",
        "  \u003ctd\u003e\n",
        "    \u003ca target=\"_blank\" href=\"https://colab.research.google.com/github/tensorflow/probability/blob/master/tensorflow_probability/examples/jupyter_notebooks/Bayesian_Switchpoint_Analysis.ipynb\"\u003e\u003cimg src=\"https://www.tensorflow.org/images/colab_logo_32px.png\" /\u003eRun in Google Colab\u003c/a\u003e\n",
        "  \u003c/td\u003e\n",
        "  \u003ctd\u003e\n",
        "    \u003ca target=\"_blank\" href=\"https://github.com/tensorflow/probability/blob/master/tensorflow_probability/examples/jupyter_notebooks/Bayesian_Switchpoint_Analysis.ipynb\"\u003e\u003cimg src=\"https://www.tensorflow.org/images/GitHub-Mark-32px.png\" /\u003eView source on GitHub\u003c/a\u003e\n",
        "  \u003c/td\u003e\n",
        "\u003c/table\u003e"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "5XxXGBbRgsq2"
      },
      "source": [
        "This notebook reimplements and extends the Bayesian “Change point analysis” example from the [pymc3 documentation](https://docs.pymc.io/notebooks/getting_started.html#Case-study-2:-Coal-mining-disasters)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "_mpkdys-KrTT"
      },
      "source": [
        "## Prerequisites"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {},
        "colab_type": "code",
        "id": "t_Uo-kwnGqZi"
      },
      "outputs": [],
      "source": [
        "import tensorflow as tf\n",
        "import tensorflow_probability as tfp\n",
        "from tensorflow_probability import edward2 as ed\n",
        "tfd = tfp.distributions\n",
        "tfb = tfp.bijectors\n",
        "import matplotlib.pyplot as plt\n",
        "plt.rcParams['figure.figsize'] = (15,8)\n",
        "%config InlineBackend.figure_format = 'retina'\n",
        "import numpy as np\n",
        "import pandas as pd"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "53lnVbvHKtH9"
      },
      "source": [
        "## Dataset"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "829rNEHfKyEq"
      },
      "source": [
        "The dataset is from [here](https://pymc-devs.github.io/pymc/tutorial.html#two-types-of-variables). Note, there is another version of this example [floating around](https://docs.pymc.io/notebooks/getting_started.html#Case-study-2:-Coal-mining-disasters), but it has “missing” data – in which case you’d need to impute missing values. (Otherwise your model will not ever leave its initial parameters because the likelihood function will be undefined.)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "colab": {
          "height": 529
        },
        "colab_type": "code",
        "executionInfo": {
          "elapsed": 1281,
          "status": "ok",
          "timestamp": 1546900515061,
          "user": {
            "displayName": "",
            "photoUrl": "",
            "userId": ""
          },
          "user_tz": 480
        },
        "id": "XGMvb9_DObuU",
        "outputId": "4f9342df-3e69-47b9-88db-ea1fee1c59ad"
      },
      "outputs": [
        {
          "data": {
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            "text/plain": [
              "\u003cmatplotlib.figure.Figure at 0x7fab6b0b3990\u003e"
            ]
          },
          "metadata": {
            "image/png": {
              "height": 512,
              "width": 899
            },
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "disaster_data = np.array([ 4, 5, 4, 0, 1, 4, 3, 4, 0, 6, 3, 3, 4, 0, 2, 6,\n",
        "                           3, 3, 5, 4, 5, 3, 1, 4, 4, 1, 5, 5, 3, 4, 2, 5,\n",
        "                           2, 2, 3, 4, 2, 1, 3, 2, 2, 1, 1, 1, 1, 3, 0, 0,\n",
        "                           1, 0, 1, 1, 0, 0, 3, 1, 0, 3, 2, 2, 0, 1, 1, 1,\n",
        "                           0, 1, 0, 1, 0, 0, 0, 2, 1, 0, 0, 0, 1, 1, 0, 2,\n",
        "                           3, 3, 1, 1, 2, 1, 1, 1, 1, 2, 4, 2, 0, 0, 1, 4,\n",
        "                           0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1])\n",
        "years = np.arange(1851, 1962)\n",
        "plt.plot(years, disaster_data, 'o', markersize=8);\n",
        "plt.ylabel('Disaster count')\n",
        "plt.xlabel('Year')\n",
        "plt.title('Mining disaster data set')\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "puvRMZnQLRmD"
      },
      "source": [
        "## Probabilistic Model"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "2UA6HkV0gXvb"
      },
      "source": [
        "The model assumes a “switch point” (e.g. a year during which safety regulations changed), and Poisson-distributed disaster rate with constant (but potentially different) rates before and after that switch point.\n",
        "\n",
        "The actual disaster count is fixed (observed); any sample of this model will need to specify both the switchpoint and the “early” and “late” rate of disasters.\n",
        "\n",
        "Original model from [pymc3 documentation example](https://pymc-devs.github.io/pymc/tutorial.html):\n",
        "\n",
        "$$\n",
        "\\begin{align*}\n",
        "(D_t|s,e,l)\u0026\\sim \\text{Poisson}(r_t), \\\\\n",
        "  \u0026 \\,\\quad\\text{with}\\; r_t = \\begin{cases}e \u0026 \\text{if}\\; t \u003c s\\\\l \u0026\\text{if}\\; t \\ge s\\end{cases} \\\\\n",
        "s\u0026\\sim\\text{Discrete Uniform}(t_l,\\,t_h) \\\\\n",
        "e\u0026\\sim\\text{Exponential}(r_e)\\\\\n",
        "l\u0026\\sim\\text{Exponential}(r_l)\n",
        "\\end{align*}\n",
        "$$\n",
        "\n",
        "However, the mean disaster rate $r_t$ has a discontinuity at the switchpoint $s$, which makes it not differentiable. Thus it provides no gradient signal to the Hamiltonian Monte Carlo (HMC) algorithm – but because the $s$ prior is continuous, HMC’s fallback to a random walk is good enough to find the areas of high probability mass in this example.\n",
        "\n",
        "As a second model, we modify the original model using a [sigmoid “switch”](https://en.wikipedia.org/wiki/Sigmoid_function) between *e* and *l* to make the transition differentiable, and use a continuous uniform distribution for the switchpoint $s$.  (One could argue this model is more true to reality, as a “switch” in mean rate would likely be stretched out over multiple years.) The new model is thus:\n",
        "\n",
        "$$\n",
        "\\begin{align*}\n",
        "(D_t|s,e,l)\u0026\\sim\\text{Poisson}(r_t), \\\\\n",
        " \u0026 \\,\\quad \\text{with}\\; r_t = e + \\frac{1}{1+\\exp(s-t)}(l-e) \\\\\n",
        "s\u0026\\sim\\text{Uniform}(t_l,\\,t_h) \\\\\n",
        "e\u0026\\sim\\text{Exponential}(r_e)\\\\\n",
        "l\u0026\\sim\\text{Exponential}(r_l)\n",
        "\\end{align*}\n",
        "$$\n",
        "\n",
        "In the absence of more information we assume $r_e = r_l = 1$ as parameters for the priors. We’ll run both models and compare their inference results."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {},
        "colab_type": "code",
        "id": "TGIiP8niPHxr"
      },
      "outputs": [],
      "source": [
        "def disaster_count_model_switch():\n",
        "  early_disaster_rate = ed.Exponential(rate=1., name='early_disaster_rate')\n",
        "  late_disaster_rate = ed.Exponential(rate=1., name='late_disaster_rate')\n",
        "  switchpoint = ed.Uniform(low=0., high=tf.to_float(len(years)),\n",
        "                           name='switchpoint')\n",
        "  def disaster_rate(ys):\n",
        "    return [tf.where(y \u003c switchpoint, early_disaster_rate, late_disaster_rate)\n",
        "            for y in ys]\n",
        "  disaster_count = ed.Poisson(rate=disaster_rate(np.arange(len(years))),\n",
        "                              name='disaster_count')\n",
        "  return disaster_count\n",
        "\n",
        "def disaster_count_model_sigmoid():\n",
        "  early_disaster_rate = ed.Exponential(rate=1., name='early_disaster_rate')\n",
        "  late_disaster_rate = ed.Exponential(rate=1., name='late_disaster_rate')\n",
        "  switchpoint = ed.Uniform(low=0., high=tf.to_float(len(years)),\n",
        "                           name='switchpoint')\n",
        "  def disaster_rate(ys):\n",
        "    return (early_disaster_rate +\n",
        "            tf.sigmoid((tf.to_float(ys)-switchpoint)) *\n",
        "            (late_disaster_rate - early_disaster_rate))\n",
        "  disaster_count = ed.Poisson(rate=disaster_rate(np.arange(len(years))),\n",
        "                              name='disaster_count')\n",
        "  return disaster_count\n",
        "\n",
        "\n",
        "log_joint_switch = ed.make_log_joint_fn(disaster_count_model_switch)\n",
        "log_joint_sigmoid = ed.make_log_joint_fn(disaster_count_model_sigmoid)\n",
        "\n",
        "\n",
        "def target_log_prob_fn(log_joint, switchpoint, early_disaster_rate, late_disaster_rate):\n",
        "  \"\"\"\n",
        "  Pass named parameters to log_joint function; disaster_count is the observed\n",
        "  value hence receives the constant disaster_data.\n",
        "  \"\"\"\n",
        "  named_args = {\n",
        "      'switchpoint': switchpoint,\n",
        "      'early_disaster_rate': early_disaster_rate,\n",
        "      'late_disaster_rate': late_disaster_rate,\n",
        "      'disaster_count': disaster_data,\n",
        "  }\n",
        "  return log_joint(**named_args)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "KgPr-m-FSMF2"
      },
      "source": [
        "The above code does three things:\n",
        "\n",
        "1. Define the model via Edward distributions. The `disaster_rate` functions are called with an array of `[0, ..., len(years)-1]` to produce a vector of `len(years)` random variables – the years before the `switchpoint` are `early_disaster_rate`, the ones after `late_disaster_rate` (modulo the sigmoid transition).\n",
        "1. Define the logprob function for the joint probability distribution. Each of the two function needs to be called with the four named parameters in the model and outputs the log probability of that outcome. (See below for an example.)\n",
        "1. The `target_log_prob_fn` passes the variable elements of the model from the method arguments through to the joint probability function, and specifies the fixed (“observed”) outcomes directly. To avoid duplication and because the method signatures of both logprob functions are the same, we make `target_log_prob_fn` take the desired logprob function as first argument.\n",
        "\n",
        "Here is a sanity-check that the target log prob function is sane:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "colab": {
          "height": 72
        },
        "colab_type": "code",
        "executionInfo": {
          "elapsed": 4636,
          "status": "ok",
          "timestamp": 1546900520164,
          "user": {
            "displayName": "",
            "photoUrl": "",
            "userId": ""
          },
          "user_tz": 480
        },
        "id": "OIxZCvGeHkQd",
        "outputId": "b009bb47-4119-4c24-b7a5-fcd44a23ea3a"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[-176.94559, -176.28717]\n",
            "[-371.3125, -366.88159]\n",
            "[-inf, -inf]\n"
          ]
        }
      ],
      "source": [
        "with tf.Session() as sess:\n",
        "  fs = [log_joint_switch, log_joint_sigmoid]\n",
        "  print([target_log_prob_fn(f, 40., 3., .9).eval() for f in fs])  # Somewhat likely result\n",
        "  print([target_log_prob_fn(f, 60., 1., 5.).eval() for f in fs])  # Rather unlikely result\n",
        "  print([target_log_prob_fn(f, -10., 1., 1.).eval() for f in fs]) # Impossible result"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "tuzwBtQxUAES"
      },
      "source": [
        "## HMC to do Bayesian inference\n",
        "\n",
        "We define the number of results and burn-in steps required; the code is mostly modeled after [the documentation of tfp.mcmc.HamiltonianMonteCarlo](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc/HamiltonianMonteCarlo). It uses an adaptive step size (otherwise the outcome is very sensitive to the step size value chosen). We use values of one as the initial state of the chain.\n",
        "\n",
        "This is not the full story though. If you go back to the model definition above, you’ll note that some of the probability distributions are not well-defined on the whole real number line. Therefore we constrain the space that HMC shall examine by wrapping the HMC kernel with a [TransformedTransitionKernel](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc/TransformedTransitionKernel) that specifies the forward bijectors to transform the real numbers onto the domain that the probability distribution is defined on (see comments in the code below)."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {},
        "colab_type": "code",
        "id": "_V57TSedc8wb"
      },
      "outputs": [],
      "source": [
        "num_results = 10000\n",
        "num_burnin_steps = 3000\n",
        "\n",
        "def make_chain(i, target_log_prob):\n",
        "  with tf.variable_scope(\"params\", reuse=tf.AUTO_REUSE):\n",
        "    step_size = tf.get_variable(\n",
        "      name='step_size_model{}'.format(i),\n",
        "      initializer=1.,\n",
        "      trainable=False)\n",
        "    step_size_adaptation_step_counter = tf.get_variable(\n",
        "      name='step_size_adaptation_step_counter{}'.format(i),\n",
        "      initializer=-1,\n",
        "      dtype=tf.int32,\n",
        "      trainable=False)\n",
        "\n",
        "  states, _ = tfp.mcmc.sample_chain(\n",
        "      num_results=num_results,\n",
        "      num_burnin_steps=num_burnin_steps,\n",
        "      current_state=[\n",
        "          # The three latent variables\n",
        "          tf.ones([], name='init_switchpoint'),\n",
        "          tf.ones([], name='init_early_disaster_rate'),\n",
        "          tf.ones([], name='init_late_disaster_rate'),\n",
        "      ],\n",
        "      kernel=tfp.mcmc.TransformedTransitionKernel(\n",
        "          inner_kernel=tfp.mcmc.HamiltonianMonteCarlo(\n",
        "            target_log_prob_fn=target_log_prob,\n",
        "            step_size=step_size,\n",
        "            step_size_update_fn=tfp.mcmc.make_simple_step_size_update_policy(\n",
        "              num_adaptation_steps=int(0.8*num_burnin_steps),\n",
        "              step_counter=step_size_adaptation_step_counter),\n",
        "            num_leapfrog_steps=3),\n",
        "          bijector=[\n",
        "              # The switchpoint is constrained between zero and len(years).\n",
        "              # Hence we supply a bijector that maps the real numbers (in a\n",
        "              # differentiable way) to the interval (0;len(yers))\n",
        "              tfb.Chain([tfb.AffineScalar(scale=tf.to_float(len(years))),\n",
        "                         tfb.Sigmoid()]),\n",
        "              # Early and late disaster rate: The exponential distribution is\n",
        "              # defined on the positive real numbers\n",
        "              tfb.Softplus(),\n",
        "              tfb.Softplus(),\n",
        "          ]))\n",
        "  return states\n",
        "\n",
        "switchpoint, early_disaster_rate, late_disaster_rate = zip(\n",
        "    make_chain(0, lambda *args: target_log_prob_fn(log_joint_switch, *args)),\n",
        "    make_chain(1, lambda *args: target_log_prob_fn(log_joint_sigmoid, *args)))\n",
        "switchpoint_, early_disaster_rate_, late_disaster_rate_ = (\n",
        "    [None, None], [None, None], [None, None])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "6QLlqXi1VHLQ"
      },
      "source": [
        "Run both models in parallel:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {},
        "colab_type": "code",
        "id": "JkDzXzcOq-3k"
      },
      "outputs": [],
      "source": [
        "init_op = tf.global_variables_initializer()\n",
        "with tf.Session() as sess:\n",
        "  init_op.run()\n",
        "  [\n",
        "    switchpoint_[0], switchpoint_[1],\n",
        "    early_disaster_rate_[0], early_disaster_rate_[1],\n",
        "    late_disaster_rate_[0], late_disaster_rate_[1],\n",
        "  ] = sess.run([\n",
        "    switchpoint[0], switchpoint[1],\n",
        "    early_disaster_rate[0], early_disaster_rate[1],\n",
        "    late_disaster_rate[0], late_disaster_rate[1],\n",
        "  ])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "G22O89uhaeKS"
      },
      "source": [
        "## Visualize the result\n",
        "\n",
        "We visualize the result as histograms of samples of the posterior distribution for the early and late disaster rate, as well as the switchpoint. The histograms are overlaid with a solid line representing the sample median, as well as the 95%ile credible interval bounds as dashed lines."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "colab": {
          "height": 1596
        },
        "colab_type": "code",
        "executionInfo": {
          "elapsed": 6320,
          "status": "ok",
          "timestamp": 1546900700089,
          "user": {
            "displayName": "",
            "photoUrl": "",
            "userId": ""
          },
          "user_tz": 480
        },
        "id": "ZzSxHMRaXoip",
        "outputId": "17af3bdc-95a1-4999-f891-bf466264676d"
      },
      "outputs": [
        {
          "data": {
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t6YMPPkCfPn2wd+9exMTE4PTp00hOTsbVq1cRFhaG+fPno2/fvgAsr1tTzmUslUoFAHjz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\nzZoVTz/9dHz00Ufd1vLd73432tra4g//8A/jd3/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            "text/plain": [
              "\u003cmatplotlib.figure.Figure at 0x7fab66e4a910\u003e"
            ]
          },
          "metadata": {
            "image/png": {
              "height": 526,
              "width": 891
            },
            "tags": []
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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LWdOn6i0mJgYXL16Et7c3PD09Kzs7FaamnReFhYWYMWMG7t+/j7Zt2+LLL79E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\nmirY2VGzCay7/rElJm7VWOpkJ/4A+4/JwFDUShl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            "text/plain": [
              "\u003cmatplotlib.figure.Figure at 0x7fab6b149590\u003e"
            ]
          },
          "metadata": {
            "image/png": {
              "height": 526,
              "width": 882
            },
            "tags": []
          },
          "output_type": "display_data"
        },
        {
          "data": {
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RrFkzqFQqqFQqZZ7U69ev693XUE9auQHUy8tL6dFYkiRJSqO3sc+bJfcQQyy9Pux1vRIR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\nZvD9fr18vbb7edbzrGezZs36znevtVJdXZ0HH3y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            "text/plain": [
              "\u003cmatplotlib.figure.Figure at 0x7fab69e60510\u003e"
            ]
          },
          "metadata": {
            "image/png": {
              "height": 526,
              "width": 903
            },
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "def _desc(v):\n",
        "  return '(median: {}; 95%ile CI: $[{}, {}]$)'.format(\n",
        "      *np.round(np.percentile(v, [50, 2.5, 97.5]), 2))\n",
        "\n",
        "for t, v in [\n",
        "    ('Early disaster rate ($e$) posterior samples', early_disaster_rate_),\n",
        "    ('Late disaster rate ($l$) posterior samples', late_disaster_rate_),\n",
        "    ('Switch point ($s$) posterior samples', years[0] + switchpoint_),\n",
        "]:\n",
        "  fig, ax = plt.subplots(nrows=1, ncols=2, sharex=True)\n",
        "  for (m, i) in (('Switch', 0), ('Sigmoid', 1)):\n",
        "    a = ax[i]\n",
        "    a.hist(v[i], bins=50)\n",
        "    a.axvline(x=np.percentile(v[i], 50), color='k')\n",
        "    a.axvline(x=np.percentile(v[i], 2.5), color='k', ls='dashed', alpha=.5)\n",
        "    a.axvline(x=np.percentile(v[i], 97.5), color='k', ls='dashed', alpha=.5)\n",
        "    a.set_title(m + ' model ' + _desc(v[i]))\n",
        "  fig.suptitle(t)\n",
        "  plt.show()"
      ]
    }
  ],
  "metadata": {
    "colab": {
      "collapsed_sections": [],
      "name": "Bayesian Switchpoint Analysis",
      "provenance": [],
      "version": "0.3.2"
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}
